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And since there are many kinds of behavior that do not return to such predictable forms after any limited number of steps, one must conclude that additive rules cannot be universal.

At the end of the last section I mentioned rule 54 as another elementary cellular automaton besides rule 110 that might be class 4. The pictures below show examples of the typical behavior of rule 54.

Captions on this page:

Two views of the evolution of rule 54 from typical random initial conditions. The top view shows the color of every cell at every step. The bottom groups together pairs of cells, and shows only every other step. There are various localized structures—and hints of class 4 behavior.

From Stephen Wolfram: A New Kind of Science [citation]